Question 1204167
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According to the Remainder theorem, the remainder is the value of the polynomial at x = -6


    remainder = 6*(-6)^2 + 31*(-6) - 29 = 1.



Next, make these identical transformations 

    6x^2 + 31x - 29 = (6x^2 + 36x) - (5x + 29) = 6x*(x+6) - (5x+30) + 1 = 6x*(x+6) - 5(x+6) + 1 = (6x-5)*(x+6) + 1.


It shows that the quotient is 6x-5 and the remainder is 1.    <U>ANSWER</U>
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Solved.